The ORF definition has some small differences in bacteria and eukaryotes. Since bacteria have very few genes with introns, an ORF is usually the entire gene coding for a probable protein meaning there is a start codon and a stop codon and close the ORF, regulatory and stoping elements should be found. In bacteria you might also find several ORF close together and sometimes overlapping. This is an operon. In eukaryotes, ORF are usually the exons.

An ORF is the reading frame from which DNA is translated into RNA. The initiation codon would be in the first exon and the termination codon in the last. The introns are not spliced out until after the transcription, so I think they do belong to the ORF.

An open reading frame (ORF) is a portion of a gene’s sequence that contains a sequence of bases, uninterrupted by stop sequences, that could potentially encode a protein. When a new gene is identified and its DNA sequence deciphered, it is still unclear what its corresponding protein sequence is. This is because, in the absence of any other knowledge, the DNA sequence can be translated or read in six possible reading frames (three for each strand, corresponding to three different start positions for the first codon). ORF identification involves scanning each of the six reading frames and determining which one(s) contains a stretch of DNA sequence bounded by a start and stop codon, yet containing no start or stop codons within it; a sequence meeting these conditions could correspond to the actual single product of the gene. The identification of an ORF provides the first evidence that a new sequence of DNA is part or all of a gene encoding for a particular protein. Source : Celera